The new floricane-fruiting cultivar of blackberry called ‘Osage’ is described herein. The new cultivar originated from a hand-pollinated cross of Arkansas selections ‘A-1719’×‘A-2108’ made in 2000. The seeds resulting from this controlled hybridization were germinated in a greenhouse in the spring of 2001 and planted in a field near Clarksville, Ark. (West-Central Arkansas). The seedlings fruited in the summer of 2003 and one seedling, designated ‘A-2362’, was selected in 2003 for its excellent flavor, thornless canes, even drupelet fill and lack of white drupelets on berries, medium berry size, excellent postharvest storage potential, mid-early season ripening, high yields and healthy plants.